Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$

TL;DR

This paper extends a valence bond algorithm to compute properties of antiferromagnetic ground states with total spin 1/2, enabling analysis of systems with odd size and free boundaries.

Contribution

The authors generalize the singlet sector valence bond algorithm to handle antiferromagnetic ground states with total spin 1/2, allowing new calculations for such systems.

Findings

Successfully calculated ground state spin texture.

Determined bond energies in odd-sized Heisenberg antiferromagnets.

Demonstrated the method's effectiveness on finite systems.

Abstract

We develop a generalization of the singlet sector valence bond basis projection algorithm of Sandvik, Beach, and Evertz (A. W. Sandvik, Phys. Rev. Lett. 95, 207203 (2005); K. S. D. Beach and A. W. Sandvik, Nucl. Phys. B750, 142 (2006); A. W. Sandvik and H. G. Evertz, arXiv:0807.0682, unpublished.) to cases in which the ground state of an antiferromagnetic Hamiltonian has total spin $S_{tot} = 1/2$ in a finite size system. We explain how various ground state expectation values may be calculated by generalizations of the estimators developed in the singlet case, and illustrate the power of the method by calculating the ground state spin texture and bond energies in a $L \times L$ Heisenberg antiferromagnet with $L$ odd and free boundaries.